Flipping one textured face of an object
Use UV coordinates instead of normal.  Then unwrap the flag with  u > unwrap.  Then in the UV image editor, while still in edit mode, scale the UV map along the horizontal axis by -1:  s > x > -1.  Scaling by -1 should flip the image.

Update:  Misunderstood the question.  I modified your node setup. This should make an un-flipped image appear on the back of the face.